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In this paper, we study pseudo-labelling. Pseudo-labelling employs raw inferences on unlabelled data as pseudo-labels for self-training. We elucidate the empirical successes of pseudo-labelling by establishing a link between this technique…
We study the large scale geometry of the mapping class group, MCG. Our main result is that for any asymptotic cone of MCG, the maximal dimension of locally compact subsets coincides with the maximal rank of free abelian subgroups of MCG. An…
In a recent paper, the authors proposed a general methodology for probabilistic learning on manifolds. The method was used to generate numerical samples that are statistically consistent with an existing dataset construed as a realization…
We investigate the properties of a class of piecewise-fractional maps arising from the introduction of an invariance under rescaling into convex quadratic maps. The subsequent maps are quasiconvex, and pseudoconvex on specific convex cones;…
Semi-supervised learning (SSL) has achieved great success in leveraging a large amount of unlabeled data to learn a promising classifier. A popular approach is pseudo-labeling that generates pseudo labels only for those unlabeled data with…
Through the use of examples, we explain one way in which applied topology has evolved since the birth of persistent homology in the early 2000s. The first applications of topology to data emphasized the global shape of a dataset, such as…
Modern graph or network datasets often contain rich structure that goes beyond simple pairwise connections between nodes. This calls for complex representations that can capture, for instance, edges of different types as well as so-called…
We focus on spectral clustering of unlabeled graphs and review some results on clustering methods which achieve weak or strong consistent identification in data generated by such models. We also present a new algorithm which appears to…
Compressive learning is a framework where (so far unsupervised) learning tasks use not the entire dataset but a compressed summary (sketch) of it. We propose a compressive learning classification method, and a novel sketch function for…
We introduce a general method to count unlabeled combinatorial structures and to efficiently generate them at random. The approach is based on pointing unlabeled structures in an "unbiased" way that a structure of size n gives rise to n…
Exemplar learning is a powerful paradigm for discovering visual similarities in an unsupervised manner. In this context, however, the recent breakthrough in deep learning could not yet unfold its full potential. With only a single positive…
In this paper we prove some geometric inequalities for closed surfaces in Euclidean three-space. Motivated by Gage's inequality for convex curves, we first verify that for convex surfaces the Willmore energy is bounded below by some…
We propose a realistic scenario for the unsupervised video learning where neither task boundaries nor labels are provided when learning a succession of tasks. We also provide a non-parametric learning solution for the under-explored problem…
Segmentation is often an essential intermediate step in image analysis. A volume segmentation characterizes the underlying volume image in terms of geometric information--segments, faces between segments, curves in which several faces…
In this paper, we address Novel Class Discovery (NCD), the task of unveiling new classes in a set of unlabeled samples given a labeled dataset with known classes. We exploit the peculiarities of NCD to build a new framework, named…
Parameter prediction is essential for many applications, facilitating insightful interpretation and decision-making. However, in many real life domains, such as power systems, medicine, and engineering, it can be very expensive to acquire…
We propose a novel unsupervised learning approach to 3D shape correspondence that builds a multiscale matching pipeline into a deep neural network. This approach is based on smooth shells, the current state-of-the-art axiomatic…
We investigate Learning from Label Proportions (LLP), a partial information setting where examples in a training set are grouped into bags, and only aggregate label values in each bag are available. Despite the partial observability, the…
Clustering is the task of gathering similar data samples into clusters without using any predefined labels. It has been widely studied in machine learning literature, and recent advancements in deep learning have revived interest in this…
Conserved charges in theories with gauge symmetries are supported on codimension-2 surfaces in the bulk spacetime. It has recently been suggested that various classical formulations of gravity dynamics display different symmetries, and…